Figure a shows the geometry of image formation by a double convex lens. Derive a generalized lens maker s equation to replace the equation 1fn. You calculate how it changes on the first boundary that s some insight that says that one creates some image of the original object and the redirected photons seem to come from the image. The lensmaker s equation relates the focal length of a simple lens with the spherical curvature of its two faces. Fermats principle to derive lens formula physics forums. For the past 1 hour, im trying to derive lens makers equation using fermats principle, which of course is our homework. Lets place the origin at the center of the lens and let right hand side be positive and left negative. Lensmakers equation wolfram demonstrations project. For the past 1 hour, im trying to derive lens maker s equation using fermat s principle, which of course is our homework.
The word lens comes from lens, the latin name of the lentil, because a doubleconvex lens is lentilshaped. Isaac physics a project designed to offer support and activities in physics problem solving to teachers and students from gcse y11, through to university. Notice that 1q is the final curvature cf, of the wave front after the wave front has passed the lens. For a double convex lens the radius r 1 is positive since it is measured. The lentil plant also gives its name to a geometric figure some scholars argue that the archeological evidence indicates that there was widespread.
If fermat s principle says that light takes the fastest path, which path is that. Lens power in diopters m1 is equal to 1f, where f is the focal length expressed in meters. If lens is not immersed in ambient medium, value of refractive index of. Ci 1 p 1i 1 v 1 as the lens is thin cc 1 p 1c 1 r 1. If a lens is thicker than that measure, the thin lens equation cannot be used. Lens manufacturers use the lens makers formula to manufacture lenses of the desired focal length. Image formed due to reflection on a spherical surface. Onsider a lens having index of refraction n2 and s. Lens makers formula using the positive optical sign convention, the lens makers formula states where f is the focal length, n is the index of refraction, and and. You calculate how it changes on the first boundary thats some insight that says that one creates some image of the original object and the redirected photons seem to come from the image.
A simple lens consists of a single piece of material, while a compound lens consists of several simple lenses elements, usually along a common axis. Lens makers formula and limitations of lens makers. The lensmakers equation relates the focal length of a simple lens with the spherical curvature of its two faces. Thick lens formula from eric weissteins world of physics. The following formula, called the lensmaker equation, is used to determine whether a lens will behave as a converging or diverging lens based on the curvature of its faces and the relative indices of the lens material n 1 and the surrounding medium n 2. Otherwise, replace n with the ratio of the refractive indices. This lens makers equation 1 solved for r 1 r 1 calculates the radius of curvature of the objectfacing side of a lens given its geometry and surroundings.
Ciconverging lens di tdivergent lens lens makers equation note that this assumes that the lens is placed in air. It is used for determining the focal length of a thin lens thickness 0 with radii of curvature r1 and r2. Derivation of lens maker formula for a concave lens. The lens makers equation is another formula used for lenses that. Homework statement a plane convex lens is made of glass index 1. Lens makers equation light rays from a beam source, initially in air, are incident on a material of different index of refraction position is given in centimeters. Lens maker s formula using the positive optical sign convention, the lens maker s formula states where f is the focal length, n is the index of refraction, and and are the radii of curvature of the two sides of the lens. Lens makers formula from eric weissteins world of physics. Consider a convex lens or concave lens of absolute refractive index m 2 to be placed in a rarer medium of absolute refractive index m 1. Lens maker s equation light rays from a beam source, initially in air, are incident on a material of different index of refraction position is given in centimeters.
The refractive index of the material of the lens a can be introduced into the lens formula. Using the formula for refraction at a single spherical surface we can say that, for the first surface, for the second surface, now adding equation 1 and 2, when u. For a thin lens, the power is approximately the sum of the surface powers. How does the lens formula follow from fermats principle. O c 1 ii c 2 1 p 1 p 2 i2 b e a d u1 v1 v2 r1 r2 t n1 t. Lens makers formula refraction by a lens a relation between the focal length of a lens, radii of curvature of two surfaces and the refractive index of the material is called lens makers formula. For more information on and versions of the lens makers equation, please see the lens makers equation calculator page. A lens is a transmissive optical device which affects the focusing of a light beam through refraction. Use the lensmakers equation 1f n11r1 1r2 to find the focal length of a double convex lens manufactured from crown glass, n 1. Derive a generalized lens makers equation to replace the equation 1fn. Note we are using the real is positive sign convention here. Commonly it is given in the thin lens limit, where it is assumed that the thickness of the lens is small compared to the object and image distances. Three important instances of equation 1, depicted in figure 3, should be kept in mind. Lensmaker equation calculator, calculate lens focal length.
For more information on and versions of the lens maker s equation, please see the lens maker s equation calculator page. Question about lens makers formula physics stack exchange. The radii of curvature here are measured according to the cartesian sign convention. Picture the problem we can use the lens makers equation to find the focal length of each of the lenses described in the problem statement. The lentil plant also gives its name to a geometric figure some scholars argue that the archeological evidence indicates that there was widespread use of lenses in antiquity, spanning several millennia.
Now using this i have to derive lens makers formula. Lenses of different focal length are used for different optical instruments. The complete derivation of lens maker formula is described below. It follows from the refraction due to convex spherical surface xp 1y. Lensmaker equation is used to determine whether a lens will behave as a converging or diverging lens based on the curvature of its faces and the relative indices of the lens material and the surrounding medium. Derivation of lens makers formula 62582 the lens makers derivation assumes some condition, they are thin lens is used for measure the distance from surface poles to lens optical centre distance. Jan 21, 2014 for the love of physics walter lewin may 16, 2011 duration. Byu cleanroom thin lens calculations for optical devices. Feb 02, 2007 homework statement a plane convex lens is made of glass index 1. Applying the equation of paraxial refraction with air to each surface gives 1 2. Ci 1 p 1 i 1 v 1 as the lens is thin cc 1 p 1 c 1 r 1. If the lens is biconvex or planoconvex, a collimated beam of light passing through the lens will be converged or focused to a spot behind. Use the lensmaker s equation 1f n11r1 1r2 to find the focal length of a double convex lens manufactured from crown glass, n 1. The refracted ray from a suffers a second refraction on the surface xp 2y and emerges along bi.
Simple thin lenses are designed by using the socalled lens makers formula. Let a concave lens have two spherical surfaces x 1 p 1 y 1 and x 2 p 2 y 2 having radius of curvature as r 1 and r 2 respectively. Considering the approximations used, we should not expect this formula to. The lensmakers formula works with this convention, although you can modify the formula and define your reference system accordingly.
Lens makers formula definition, formula and solved examples. First, when p q, then both the object and image are 2f from the lens. It is used for determining the focal length of a thin lens thickness. Point e is the center of curvature of the right surface of the lens and ed is normal to the surface. For the love of physics walter lewin may 16, 2011 duration. Let o be a point object lying in the rarer medium on the principal axis of the. A lens has two curved surfaces, but both are not exactly same. We assume a thin, converging lens and that the light rays we are dealing with are close to the principal axis and make very small angles with the principal axis angles of less than 10 o, resulting in very small angles of incidence. Derivation of lens maker formula detailed lens maker. Make a sketch of each lens and find each focal length in air. Now we would like to reinterpret the meaning of the usual lens formula. Oct 07, 2014 here s a picture of light going through a lens index of refraction of 1. Due to the geometrical symmetry, the thin lens equation can be used for a convex and concave mirrors.
Notes on lens makers formula and combination of thin lenses. A thin lens is defined as a lens with a thickness that is approximately ignorable compared with the radii of curvature of the lens. If fermats principle says that light takes the fastest path, which path is that. The lens maker formula is utilized to create a lens with a defined focal length. Considering the refraction of a point object on the surface xp 1 y, the image is formed at i 1 who is at a distance of v 1. By using the lens makers formula you can determine the focal length of the specific lens if you know the parameters such as refractive index and radius of curvature. A lens has two foci, f and, on either side of it by the sign convention. The focal length of a lens depends on the refractive index of the lens and the radii of curvature. Heres a picture of light going through a lens index of refraction of 1. If the answer is not available please wait for a while and a community member will probably answer this soon. Check the limitations of the lens makers formula to understand the lens maker formula derivation is a. The questions and answers of how to derive lens makers formula. As b and d both are close to the optical centre of the lens, bo. If lens is not immersed in ambient medium, value of refractive index of ambient medium is 1.
You can change the curvature of the surface of the material as well as the index of refraction. The lensmakers equation links the radii of curvature of two sides of a lens, the refractive index of the material from which it is made and the focal length of the lens. This equation is used for determining the focal length of a thin lens thickness 0 with radii of curvature r1 and r2. Nov 06, 2019 this lens maker s equation 1 solved for r 1 r 1 calculates the radius of curvature of the objectfacing side of a lens given its geometry and surroundings.
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